A Cutting Plane Approach for Solving Linear Bilevel Programming Problems

Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric optimization problem as part of their constraints. From the mathematical point of view, the BLP problem is NP-hard even if the objectives and constraints are linear. This paper proposes a cutting plane approach to solve linear BLP problem which is the simplest case of BLP problems. Our approach is based on the idea that is commonly used in computational mathematics: solving a relaxation problem that is easier to solve and giving a tight approximation by introduction of cutting planes. Therefore, by exploring the theoretical properties of linear BLP, we extend the cutting plane approach for solving linear BLP problems. Numerical examples are provided to illustrate the approach.